Rate law for the reaction `A + 2B to C `is found to be Rate =k[A][B] Concentration of reactant 'B' is doubled. Keeping the concentration of 'A' constant, the value of rate constant will be:

Options

A. the same
B. doubled
C. quadrupled
D. halved

Explanation

To solve the problem, we need to analyze the effect of changing the concentration of reactant B on the rate constant of the reaction. The reaction given is:

\[ A + 2B \rightarrow C \]

The rate law for this reaction is given as:

\[ \text{Rate} = k[A][B] \]

Where:
- \( k \) is the rate constant,
- \([A]\) is the concentration of reactant A,
- \([B]\) is the concentration of reactant B.

### Step-by-Step Solution:

1. **Understand the Rate Law**: The rate law indicates that the rate of the reaction depends on the concentrations of reactants A and B. The order of the reaction with respect to A is 1, and with respect to B is also 1. Therefore, the overall order of the reaction is 2.

2. **Initial Rate Expression**: The initial rate of the reaction can be expressed as:
\[ R = k[A][B] \]

3. **Change in Concentration of B**: According to the problem, the concentration of B is doubled while keeping the concentration of A constant. Therefore, if the initial concentration of B is \([B]\), the new concentration of B becomes \(2[B]\).

4. **New Rate Expression**: With the new concentration of B, the rate of the reaction becomes:
\[ R' = k[A][2B] = k[A](2[B]) = 2k[A][B] \]

5. **Effect on Rate**: The new rate \(R'\) is twice the initial rate \(R\):
\[ R' = 2R \]
This indicates that the rate of the reaction has doubled due to the increase in the concentration of B.

6. **Rate Constant**: The rate constant \(k\) is a proportionality constant that is dependent on the temperature and the nature of the reaction, but it does not change with the concentration of reactants. Therefore, even though the rate has changed, the value of the rate constant \(k\) remains the same.

### Conclusion:
The value of the rate constant \(k\) remains unchanged when the concentration of reactant B is doubled while keeping the concentration of A constant.

### Final Answer:
The value of the rate constant \(k\) will remain the same.

---